Details

Time bar (total: 14.1s)

sample470.0ms

Algorithm
intervals
Results
382.0ms3861×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune18.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.2b

Counts
2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt times-frac
63×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
22×add-exp-log add-cbrt-cube
14×pow1
13×swap-sqr associate-*r* associate-*l*
8×div-inv
6×cbrt-undiv pow-unpow div-exp
4×pow-exp prod-exp cbrt-unprod add-log-exp rem-cube-cbrt unswap-sqr
3×sqrt-prod
2×cube-div cube-mult pow-to-exp pow-pow unpow3 sqr-pow
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up
Counts
4 → 172
Calls
4 calls:
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series88.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
30.0ms
(pow (/ 1.0 (fabs x)) 3)
31.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify125.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
05841144
13655959
25001912

prune988.0ms

Filtered
182 candidates to 100 candidates (54.9%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New16319182
Fresh011
Picked101
Done000
Total16420184

Merged error: 0.4b

Counts
184 → 20

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
98×times-frac
76×add-cube-cbrt *-un-lft-identity
31×add-exp-log add-cbrt-cube
26×swap-sqr associate-*r* associate-*l*
20×pow1
13×unpow-prod-down cube-prod
10×div-inv
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod unswap-sqr
4×add-log-exp
3×pow-unpow sqrt-prod
2×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ pow-exp pow-sqr *-commutative pow-prod-up rem-cube-cbrt
1×cube-div cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 sqr-pow
Counts
4 → 193
Calls
4 calls:
10.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series76.0ms

Counts
4 → 10
Calls
4 calls:
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
21.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify106.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
05351298
133211112
25001972

prune992.0ms

Filtered
203 candidates to 119 candidates (58.6%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New18914203
Fresh11819
Picked101
Done000
Total20122223

Merged error: 0.2b

Counts
223 → 22

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0))))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log
62×add-sqr-sqrt
58×frac-times times-frac
49×add-cube-cbrt *-un-lft-identity
37×prod-exp add-cbrt-cube
34×associate-*l/
32×associate-*r/
29×div-exp
28×frac-add
18×pow1
16×associate-*r*
14×associate-*l*
13×unpow-prod-down cube-prod swap-sqr cbrt-unprod
10×pow-exp
9×cbrt-undiv pow-to-exp
6×div-inv
4×flip3-+ pow-prod-down flip-+ add-log-exp unswap-sqr
3×pow-unpow sqrt-prod
2×*-commutative rem-cube-cbrt
1×cube-div pow2 distribute-rgt-in cube-mult rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 203
Calls
4 calls:
23.0ms
(* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0))))
10.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series178.0ms

Counts
4 → 10
Calls
4 calls:
125.0ms
(* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0))))
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify58.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014162567
150012227

prune1.1s

Filtered
213 candidates to 126 candidates (59.2%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New2049213
Fresh14721
Picked101
Done000
Total21916235

Merged error: 0.1b

Counts
235 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (+ (+ (/ (* (* 1.0 1.0) (+ (* 3.0 (* (fabs x) 8.0)) (* 4.0 (* (* 1.0 (/ 1.0 (fabs x))) 15.0)))) (* (* (* (pow (fabs x) 4) (fabs x)) (* (fabs x) 8.0)) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.4b
(/ (* (* 1.0 1.0) (+ (* 3.0 (* (fabs x) 8.0)) (* 4.0 (* (* 1.0 (/ 1.0 (fabs x))) 15.0)))) (* (* (* (pow (fabs x) 4) (fabs x)) (* (fabs x) 8.0)) 4.0))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
182×add-exp-log
113×prod-exp
112×add-cbrt-cube
77×times-frac
59×cbrt-unprod
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
37×div-exp
25×cbrt-undiv
23×associate-/r*
21×sqrt-prod
13×unpow-prod-down cube-prod
8×pow-exp
7×pow-to-exp associate-/l/
6×pow1 div-inv
5×associate-*l/
4×frac-add add-log-exp
3×pow-unpow flip3-+ flip-+
2×frac-2neg associate-*r/ clear-num associate-/l* rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-/r/ sqr-pow
Counts
4 → 191
Calls
4 calls:
114.0ms
(/ (* (+ (+ (/ (* (* 1.0 1.0) (+ (* 3.0 (* (fabs x) 8.0)) (* 4.0 (* (* 1.0 (/ 1.0 (fabs x))) 15.0)))) (* (* (* (pow (fabs x) 4) (fabs x)) (* (fabs x) 8.0)) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
21.0ms
(/ (* (* 1.0 1.0) (+ (* 3.0 (* (fabs x) 8.0)) (* 4.0 (* (* 1.0 (/ 1.0 (fabs x))) 15.0)))) (* (* (* (pow (fabs x) 4) (fabs x)) (* (fabs x) 8.0)) 4.0))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series558.0ms

Counts
4 → 10
Calls
4 calls:
406.0ms
(/ (* (+ (+ (/ (* (* 1.0 1.0) (+ (* 3.0 (* (fabs x) 8.0)) (* 4.0 (* (* 1.0 (/ 1.0 (fabs x))) 15.0)))) (* (* (* (pow (fabs x) 4) (fabs x)) (* (fabs x) 8.0)) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
120.0ms
(/ (* (* 1.0 1.0) (+ (* 3.0 (* (fabs x) 8.0)) (* 4.0 (* (* 1.0 (/ 1.0 (fabs x))) 15.0)))) (* (* (* (pow (fabs x) 4) (fabs x)) (* (fabs x) 8.0)) 4.0))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify78.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014515626
150014726

prune883.0ms

Filtered
201 candidates to 110 candidates (54.7%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1947201
Fresh9615
Picked011
Done000
Total20314217

Merged error: 0.1b

Counts
217 → 14

regimes426.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample7.6s

Algorithm
intervals
Results
6.4s66381×body80valid

Profiling

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